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Annotation of 43BSDTahoe/usr.lib/libm/acosh.c, revision 1.1.1.1

1.1       root        1: /*
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * All rights reserved.
                      4:  *
                      5:  * Redistribution and use in source and binary forms are permitted
                      6:  * provided that the above copyright notice and this paragraph are
                      7:  * duplicated in all such forms and that any documentation,
                      8:  * advertising materials, and other materials related to such
                      9:  * distribution and use acknowledge that the software was developed
                     10:  * by the University of California, Berkeley.  The name of the
                     11:  * University may not be used to endorse or promote products derived
                     12:  * from this software without specific prior written permission.
                     13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     16:  *
                     17:  * All recipients should regard themselves as participants in an ongoing
                     18:  * research project and hence should feel obligated to report their
                     19:  * experiences (good or bad) with these elementary function codes, using
                     20:  * the sendbug(8) program, to the authors.
                     21:  */
                     22: 
                     23: #ifndef lint
                     24: static char sccsid[] = "@(#)acosh.c    5.3 (Berkeley) 6/30/88";
                     25: #endif /* not lint */
                     26: 
                     27: /* ACOSH(X)
                     28:  * RETURN THE INVERSE HYPERBOLIC COSINE OF X
                     29:  * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
                     30:  * CODED IN C BY K.C. NG, 2/16/85;
                     31:  * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85.
                     32:  *
                     33:  * Required system supported functions :
                     34:  *     sqrt(x)
                     35:  *
                     36:  * Required kernel function:
                     37:  *     log1p(x)                ...return log(1+x)
                     38:  *
                     39:  * Method :
                     40:  *     Based on 
                     41:  *             acosh(x) = log [ x + sqrt(x*x-1) ]
                     42:  *     we have
                     43:  *             acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else           
                     44:  *             acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
                     45:  *     These formulae avoid the over/underflow complication.
                     46:  *
                     47:  * Special cases:
                     48:  *     acosh(x) is NaN with signal if x<1.
                     49:  *     acosh(NaN) is NaN without signal.
                     50:  *
                     51:  * Accuracy:
                     52:  *     acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
                     53:  *     rounded. In a test run with 512,000 random arguments on a VAX, the
                     54:  *     maximum observed error was 3.30 ulps (units of the last place) at
                     55:  *     x=1.0070493753568216 .
                     56:  *
                     57:  * Constants:
                     58:  * The hexadecimal values are the intended ones for the following constants.
                     59:  * The decimal values may be used, provided that the compiler will convert
                     60:  * from decimal to binary accurately enough to produce the hexadecimal values
                     61:  * shown.
                     62:  */
                     63: 
                     64: #if defined(vax)||defined(tahoe)       /* VAX D format */
                     65: #ifdef vax
                     66: #define _0x(A,B)       0x/**/A/**/B
                     67: #else  /* vax */
                     68: #define _0x(A,B)       0x/**/B/**/A
                     69: #endif /* vax */
                     70: /* static double */
                     71: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
                     72: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
                     73: static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
                     74: static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
                     75: #define    ln2hi    (*(double*)ln2hix)
                     76: #define    ln2lo    (*(double*)ln2lox)
                     77: #else  /* defined(vax)||defined(tahoe) */
                     78: static double
                     79: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
                     80: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
                     81: #endif /* defined(vax)||defined(tahoe) */
                     82: 
                     83: double acosh(x)
                     84: double x;
                     85: {      
                     86:        double log1p(),sqrt(),t,big=1.E20; /* big+1==big */
                     87: 
                     88: #if !defined(vax)&&!defined(tahoe)
                     89:        if(x!=x) return(x);     /* x is NaN */
                     90: #endif /* !defined(vax)&&!defined(tahoe) */
                     91: 
                     92:     /* return log1p(x) + log(2) if x is large */
                     93:        if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 
                     94: 
                     95:        t=sqrt(x-1.0);
                     96:        return(log1p(t*(t+sqrt(x+1.0))));
                     97: }

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